M.M. Rahman

Boundary layer flow of a nanofluid past a permeable exponentially shrinking surface with convective boundary condition using Buongiorno’s model

Purpose – The purpose of this paper is to numerically solve the problem of steady boundary layer flow of a nanofluid past a permeable exponentially shrinking surface with convective surface condition. The Buongiorno’s mathematical nanofluid model has been used. Design/methodology/approach – Using appropriate similarity transformations, the basic partial differential equations are transformed into ordinary differential equations. These equations have been solved numerically for different values of the governing parameters, stretching/shrinking parameter λ, suction parameter s, Prandtl number Pr, Lewis number Le, Biot number, the Brownian motion parameter Nb and the thermophoresis parameter Nt, using the bvp4c function from Matlab. The effects of these parameters on the reduced skin friction coefficient, heat transfer from the surface of the sheet, Sherwood number, dimensionless velocity, and temperature and nanoparticles volume fraction distributions are presented in tables and graphs, and are in details d...

Oblique stagnation-point flow of a nanofluid past a shrinking sheet

Purpose – The laminar two-dimensional stagnation-point flow and heat transfer of a viscous incompressible nanofluid obliquely impinging on a shrinking surface is formulated as a similarity solution of the Navier-Stokes, energy and concentration equations. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The effect of the dimensionless strain rate, shrinking parameter, Brownian motion parameter and thermophoresis parameter on the flow, temperature and nanoparticle volume fraction is investigated in details. The paper aims to discuss these issues. Design/methodology/approach – The transformed system of ordinary differential equations was solved using the function bvp4c from Matlab. The relative tolerance was set to 10−10. Findings – It is found that dimensionless strain rate and shrinking parameter causes a shift in the position of the point of zero skin friction along the stretching sheet. Obliquity of the flow toward the surface increases as the strain rate ...

Buoyancy Induced Heat Transfer Flow Inside a Tilted Square Enclosure Filled with Nanofluids in the Presence of Oriented Magnetic Field

ABSTRACT This paper analyzes heat transfer and fluid flow of natural convection in an inclined square enclosure filled with different types of nanofluids having various shapes of nanoparticles in the presence of oriented magnetic field. The Galerkin weighted residual finite element method has been employed to solve the governing non-dimensional partial differential equations. In the numerical simulations, water, ethylene glycol, and engine oil containing copper, alumina, titanium dioxide nanoparticles are considered. The effects of model parameters such as Rayleigh number, Hartmann number, nanoparticles volume fraction, magnetic field inclination angle, geometry inclination angle on the fluid flow and heat transfer are investigated. The results indicate that increment of the Rayleigh number and nanoparticle volume fraction increase the heat transfer rate in a significant way, whereas, increment of the Hartmann number decreases the overall heat transfer rate. It is also observed that a blade shape nanoparticle gives higher heat transfer rate compared to other shapes of nanoparticles. The critical geometry inclination angle at which the maximum heat transfer rate is achieved depends on the nanoparticle volume fraction as well as on the magnetic field orientation. These results are new and have direct applications in solar thermal collectors and thermal insulator of buildings.

The dynamics of two interacting compositional plumes in the presence of a magnetic field

The dynamics of two compositionally buoyant columns of fluid rising in an infinite less buoyant fluid is studied in the presence of a uniform magnetic field, B 0. The fluid is thermally stably stratified and has a viscosity, ν, a thermal diffusivity, κ and magnetic diffusivity, η. The stability of the mean state to infinitesimal disturbances is governed by the seven dimensionless parameters: the Reynolds number, R (=UL/ν, where U, L are characteristic velocity and length respectively) which measures the strength of the compositional buoyancy; the dimensionless measures x 0, x 1, d of the thickness of the two plumes and the distance between them, respectively; the ratio Γ of the strengths of the two plumes (as measured by their basic concentration of light material); the Chandrasekhar number, Qc (= , in which μ is the magnetic permeability, ρ0 the fluid density and B 0 a characteristic unit of magnetic field), is a measure of the magnitude of the magnetic field and the normalized horizontal projection of the magnetic field, where θ measures the inclination of the magnetic field to the vertical. The stability is examined for small values of R. The preferred mode of instability is studied in the parameter space (x 0, x 1, d,  ). It is shown that the influence of the magnetic field does not change the order of the magnitude of the growth rate from O(R 0) of the two non-magnetic interacting plumes and it does not introduce any new modes to the stability problem. However, the presence of the magnetic field introduces novel features to the stability problem. For any fixed set x 0, x 1, d, Γ, Qc, the growth rate can either increase with or initially decrease reaching a minimum before it increases again. As Qc increases, with fixed, the growth rate can assume one of four different behaviours: (i) it maintains the same value of the non-magnetic case with the disturbance propagating along field lines; (ii) it decreases steadily with Qc; (iii) it maintains the same value as in the absence of the field until a value is reached when it starts to increase to a maximum before it decreases to zero for large values of Qc and (iv) it increases from its value for Qc = 0 reaching a maximum before it decreases steadily to zero at some value of Qc dependent on the other parameters. The helicity and α-effect have also been studied to find that the unstable motions can produce mean helicity and α-effect.

A spectral solution of nonlinear mean field dynamo equations: With inertia

This paper presents a numerical solution method for the nonlinear mean field dynamo equations in a rotating fluid spherical shell. A finite amplitude field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation, equilibrating the field. This equilibration process is a key aspect of the full hydrodynamic dynamo as well as mean field dynamo. Including full inertial term we present pseudo-spectral time-stepping procedure to solve the coupled nonlinear momentum equation and induction equation with no-slip velocity boundary conditions in the core for a finitely conducting inner core and an insulating mantle. The method is found suitable for solving many geophysical problems.